Asynchronous transfer mode (ATM) networks must define multicast capabilities in order to efficiently support numerous applications, such as video conferencing and distributed applications, in addition to LAN emulation (LANE) and Internet protocol (IP) multicasting. Several problems and issues arise in ATM multicasting, such as signaling, routing, connection admission control, and traffic management problems. IP integrated services over ATM poses further challenges to ATM multicasting. Scalability and simplicity are the two main concerns for ATM multicasting. This paper provides a survey of the current work on multicasting problems in general, and ATM multicasting in particular. A number of proposed schemes is examined, such as the schemes MARS, MCS, SEAM, SMART, RSVP, and various multipoint traffic management and transport-layer schemes. The paper also indicates a number of key open issues that remain unresolved.